Construction of digital nets from BCH-codes
We establish a link between the theory of error-correcting codes and the theory of (t, m, s)-nets. This leads to the fundamental problem of net embeddings of linear codes. Our main result is the construction of four infinite families of digital (t, m, s)-nets based on BCH- codes.
Unable to display preview. Download preview PDF.
- M. J. Adams and B. L. Shader, A construction for (t,m, s)-nets in base q, SIAM Journal of Discrete Mathematics, to appear.Google Scholar
- A. T. Clayman, K. M. Lawrence, G. L. Mullen, H. Niederreiter, and N. J. A. Sloane, Updated tables of parameters of (t,m, s)-nets, manuscript.Google Scholar
- K. M. Lawrence, A. Mahalanabis, G. L. Mullen, and W.C.H. Schmid, Construction of digital (t,m, s) -nets from linear codes, in S. Cohen and H. Niederreiter, editors, Finite Fields and Applications (Glasgow, 1995), volume 233 of Lecture Notes Series of the London Mathematical Society, pages 189–208. Cambridge University Press, Cambridge, 1996.CrossRefGoogle Scholar